Line ABC is a straight line

DanielleElmas [232]

Do cross multiply or butterfly. For example first one. 18/x=6/10 So cross multiply 18×10 =6x 180=6x Divide both sides by 6 to get x alone 180÷6=30 So x =30 Do the same to rest

4 0

3 years ago

Richard has just been given an l0-question multiple-choice quiz in his history class. Each question has five answers, of which o

myrzilka [38]

Answer:

a) 0.0000001024 probability that he will answer all questions correctly.

b) 0.1074 = 10.74% probability that he will answer all questions incorrectly

c) 0.8926 = 89.26% probability that he will answer at least one of the questions correctly.

d) 0.0328 = 3.28% probability that Richard will answer at least half the questions correctly

Step-by-step explanation:

For each question, there are only two possible outcomes. Either he answers it correctly, or he does not. The probability of answering a question correctly is independent of any other question. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Each question has five answers, of which only one is correct

This means that the probability of correctly answering a question guessing is $p = \frac{1}{5} = 0.2$

10 questions.

This means that $n = 10$

A) What is the probability that he will answer all questions correctly?

This is $P(X = 10)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} = 0.0000001024$

0.0000001024 probability that he will answer all questions correctly.

B) What is the probability that he will answer all questions incorrectly?

None correctly, so $P(X = 0)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{10,0}.(0.2)^{0}.(0.8)^{10} = 0.1074$

0.1074 = 10.74% probability that he will answer all questions incorrectly

C) What is the probability that he will answer at least one of the questions correctly?

This is

$P(X \geq 1) = 1 - P(X = 0)$

Since $P(X = 0) = 0.1074$ , from item b.

$P(X \geq 1) = 1 - 0.1074 = 0.8926$

0.8926 = 89.26% probability that he will answer at least one of the questions correctly.

D) What is the probability that Richard will answer at least half the questions correctly?

This is

$P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 5) = C_{10,5}.(0.2)^{5}.(0.8)^{5} = 0.0264$

$P(X = 6) = C_{10,6}.(0.2)^{6}.(0.8)^{4} = 0.0055$

$P(X = 7) = C_{10,7}.(0.2)^{7}.(0.8)^{3} = 0.0008$

$P(X = 8) = C_{10,8}.(0.2)^{8}.(0.8)^{2} = 0.0001$

$P(X = 9) = C_{10,9}.(0.2)^{9}.(0.8)^{1} \approx 0$

$P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} \approx 0$

So

$P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.0264 + 0.0055 + 0.0008 + 0.0001 + 0 + 0 = 0.0328$

0.0328 = 3.28% probability that Richard will answer at least half the questions correctly

8 0

3 years ago

An actor invests some money at 7%, and $48000 and more than twotimes the amount of 9%. The total annual interest earned from the

forsale [732]

Answer:

At 7% $54,000

At 9% $156,000

Step-by-step explanation:

Let x be the amount invested at 7%, Then 2x + 48000 will be the amount invested at 9%

We know that:

7% = 0.07 & 9% = 0.09

So we can write the interest equation as follows:

0.07x + 0.09 (2x + 48000) = 17820

0.07x + 0.18x + 4320 = 17820

0.25x + 4320 = 17820

Subtracting 4320 from both sides of the equation we get:

0.25x = 17820 - 4320

0.25x = 13500

Dividing both sides of the equation by 0.25 we get:

x = 13500 / 0.25

x = $54,000 invested at 7%

&

2 x 54000 + 48000

= $156,000 invested at 9%

Hence the amount invested at 7% is $54,000.

& the amount invested at 9% is $156,000.

5 0

4 years ago

A dog eats 7 oz. Of dog food in 20 minutes. At this rate, how much food can the dog eat in 2 hours?

Step2247 [10]

Answer:

bts

Step-by-step explanation:

BTSSS SSSSSSSTU6T

4 0

3 years ago

Read 2 more answers

Find whether the no. 847,2160 are coprime or not

m_a_m_a [10]

First what you need to do is find the HCF of both numbers.
After you've done that if it is 1 then they are what we call co-prime.
Now, if they are other than 1 they are not co-prime.

8 0

3 years ago